问题
I have a simple game, I'm trying to get the shortest route between 2 points
The map consists of 2d array matrix: Node[][],
class Node{
index: {
x: number,
y: number
},
isAvailable: boolean
}
The algorithm should return the shortest path with respect to node availability.
e.g. Trees are marked as unavailable node.isAvailable = false
I'm stuck on implementing the algorithm for this matrix
I tried to use Dijkstras algorithm from here, but I couldn't figure out how to apply it, I did
const graph = new Dijkstra();
//convert the matrix (2d array) to graph
matrix.map((row) => {
row.map((node: Node) => {
let x = node.index.x;
let y = node.index.y;
graph.addVertex(x + ":" + y, {x: x, y: y});
});
});
console.log(graph.shortestPath('0:0', '5:5'));
//the output was ['0:0'] (definitly not the answer)
How can I apply the algorithm on this matrix?
P.S here is my full code
回答1:
I used a method best described as spilling paint at the target:
You mark the target square with 0, then traverse the neighbours and mark them as 1, which represents distance to target, then traverse neighbours of neighbours, etc. Repeat the process until the paint reaches your troll. All that is left for troll to do is just start moving to the squares with lowest potential.
It becomes more fun once you have multiple characters that need to path around each other while everyone is moving.
回答2:
I had to implement the A* algorithm
export class PathFinder {
grid: Tile[][];
gridHeight: number;
gridWidth: number;
startTile: Tile;
endTile: Tile;
/** Array of the already checked tiles. */
closedList: List<Tile> = new List<Tile>();
openList: List<Tile> = new List<Tile>();
constructor(grid: Tile[][], gridHeight: number, gridWidth: number) {
this.grid = grid;
this.gridHeight = gridHeight;
this.gridWidth = gridWidth;
}
searchPath(start: Tile, end: Tile): Tile[] {
this.startTile = start;
this.endTile = end;
/** Path validation */
if (!start.walkable) {
console.log('The start tile in not walkable, choose different tile than', start.index);
return [];
}
if (!end.walkable) {
console.log('The end tile in not walkable, choose different tile than', end.index);
return [];
}
/** Start A* Algorithm */
/** Add the starting tile to the openList */
this.openList.push(start);
let currentTile;
/** While openList is not empty */
while (this.openList.length) {
//current node = node for open list with the lowest cost.
currentTile = this.getTileWithLowestTotal(this.openList);
//if the currentTile is the endTile, then we can stop searching
if(JSON.stringify(currentTile.index) === JSON.stringify(end.index)){
this.startTile.setBackgroundColor("rgba(255, 45, 45, .8)");
this.endTile.setBackgroundColor("rgba(255, 45, 45, .8)");
return this.shortestPath();
}
else {
//move the current tile to the closed list and remove it from the open list.
this.openList.remove(currentTile);
this.closedList.push(currentTile);
// //Get all adjacent Tiles
let adjacentTiles = this.getAdjacentTiles(currentTile);
for (let adjacentTile of adjacentTiles) {
//Get tile is not in the open list
if (!this.openList.contains(adjacentTile)) {
//Get tile is not in the closed list
if (!this.closedList.contains(adjacentTile)) {
//move it to the open list and calculate cost
this.openList.push(adjacentTile);
//calculate the cost
adjacentTile.cost = currentTile.cost + 1;
//calculate the manhattan distance
adjacentTile.heuristic = this.manhattanDistance(adjacentTile);
// calculate the total amount
adjacentTile.total = adjacentTile.cost + adjacentTile.heuristic;
currentTile.setBackgroundColor('rgba(0, 181, 93, 0.8)');
}
}
}
}
}
}
getTileWithLowestTotal(openList: Tile[]): Tile {
let tileWithLowestTotal = new Tile();
let lowestTotal: number = 999999999;
/** Search open tiles and get the tile with the lowest total cost */
for (let openTile of openList) {
if (openTile.total <= lowestTotal) {
//clone lowestTotal
lowestTotal = openTile.total;
tileWithLowestTotal = openTile;
}
}
return tileWithLowestTotal;
}
getAdjacentTiles(current: Tile): Tile[] {
let adjacentTiles: Tile[] = [];
let adjacentTile: Tile;
//Tile to left
if (current.index.x - 1 >= 0) {
adjacentTile = this.grid[current.index.x - 1][current.index.y];
if (adjacentTile && adjacentTile.walkable) {
adjacentTiles.push(adjacentTile);
}
}
//Tile to right
if (current.index.x + 1 < this.gridWidth) {
adjacentTile = this.grid[current.index.x + 1][current.index.y];
if (adjacentTile && adjacentTile.walkable) {
adjacentTiles.push(adjacentTile);
}
}
//Tile to Under
if (current.index.y + 1 < this.gridHeight) {
adjacentTile = this.grid[current.index.x][current.index.y + 1];
if (adjacentTile && adjacentTile.walkable) {
adjacentTiles.push(adjacentTile);
}
}
//Tile to Above
if (current.index.y - 1 >= 0) {
adjacentTile = this.grid[current.index.x][current.index.y - 1];
if (adjacentTile && adjacentTile.walkable) {
adjacentTiles.push(adjacentTile);
}
}
/** TODO: Diagonal moves */
return adjacentTiles;
}
/** Calculate the manhattan distance */
manhattanDistance(adjacentTile: Tile): number {
return Math.abs((this.endTile.index.x - adjacentTile.index.x) +
(this.endTile.index.y - adjacentTile.index.y));
}
shortestPath() {
let startFound: boolean = false;
let currentTile = this.endTile;
let pathTiles = [];
//includes the end tile in the path
pathTiles.push(this.endTile);
this.endTile.ball = true;
while (!startFound) {
let adjacentTiles = this.getAdjacentTiles(currentTile);
//check to see what newest current tile.
for (let adjacentTile of adjacentTiles) {
//check if it is the start tile
if (JSON.stringify(adjacentTile.index) === JSON.stringify(this.startTile.index)){
return pathTiles;
}
//it has to be inside the closedList or openList
if (this.closedList.contains(adjacentTile) || this.openList.contains(adjacentTile)) {
if (adjacentTile.cost <= currentTile.cost && adjacentTile.cost > 0) {
//change the current tile.
currentTile = adjacentTile;
//Add this adjacentTile to the path list
pathTiles.push(adjacentTile);
//highlight way with yellow balls
adjacentTile.ball = true;
break;
}
}
}
}
}
}来源：https://stackoverflow.com/questions/40857466/finding-the-shortest-path-between-two-points-in-2d-array